Though transport phenomena of solidification vary with materials, solidifying pure liquids to crystalline solids has been found to undergo five distinct stages regardless of the geometry or ambient conditions:
- Supercooling of liquid,
- Nucleation,
- Crystal growth or recalescence,
- Equilibrium freezing, and
- Subcooling of solid.
These stages can also be categorized based on the length and time scales.
We develop a multi-scale solidification framework for pure substances using laboratory experiments and mathematical modeling. Specifically, we use the analytical solution to Stefan problems at macroscale, incorporate the phase-field method for 2D crystal growth at mesoscale, and predict the spontaneous heterogeneous nucleation with an Arrhenius-type equation at microscale.
